Why Waves Never Stop

By Hartmut Neff

This is a book about the physics of space and time. The main goal of
this book is to explain why time passes slower on a moving
train. Unfortunately, this is not easy to explain. Or rather, it
cannot be explained at all.  This is, of course, a provocative
statement, whose meaning will depend on the interpretation of the word
to explain.

We will therefore first deal with explanations in themselves and
analyse the question of what it means to explain, of how explanations
work. That, you may think, is of no concern to you.  After all,
finding explanations is my job. But, we are in the same boat, as
explanations are, obviously, closely linked to how we understand. In
this context, we will encounter rules, that will be very simple in
their structure, but lead to very complicated
consequences. Understanding has more to do with the complicated
consequences than with the simple rules. This is what makes explaining
and understanding difficult.  In fact, we will even see, that those
complicated consequences cannot really be understood at all, but that
we rather just get used to them.  Understanding is therefore an
inappropriate vocabulary to describe what we are about to do in this
book, and so is explaining. This are good news, as now, there cannot
be anything in the book that cannot be understood. Instead, you just
have to get used to it. That, I think, should be doable.

Nonetheless, we will then embark on a search for explanatory models
through the history of physics. This search will be successful because
we will find the only true, the ultimate language for an objective
description of nature. What language might this be?

With this language we will explore how classical physics uses the
quantities space and time. We will wonder why it takes time to move
through space. What does time have to do with it? Waves will teach us
that space and time have to be treated on an equal footing. Shouldn't
it then take space to move through time? Shouldn't time depend on how
something is moving through space? Shouldn't time be individual,
relative and not absolute?

Time is not what we think it is.  We will discover, by looking at a
water bottle and by throwing dice, that the flow of time is an
illusion. The way physics describes time is fundamentally different
from the way we experience it, from what we think time is.

In a slightly more technical chapter, we will learn how different
observers can compare their locations and clocks, that is, space and
time, with each other and, based on that, how they can converse about
their respective views on nature. It is a curious thing that this type
of conversations, that such a theoretical argument, will directly lead
to the most famous equation of all, $E = m c^2$, with all of its
dramatic consequences for the real world.

Finally, we will learn how waves force us to treat space and time on
an equal footing and how this merges space and time into a union, into
spacetime.  Waves are, furthermore, responsible for the constant speed
of light.  Just think of your last visit to the beach. Have you ever
wondered why waves seem to always go at the same speed? Have you ever
asked yourself,

Why Waves Never Stop?

• Language: English
• Publisher: Hartmut Neff
• Release date: Jan 8, 2024
• ISBN: 9798224824632

Book preview

Chapter 1

Introduction

This is a book about the physics of space and time. The main goal of this book is to explain why time passes slower on a moving train. Unfortunately, this is not easy to explain. Or rather, it cannot be explained at all. This is, of course, a provocative statement, whose meaning will depend on the interpretation of the word to explain.

We will therefore first deal with explanations in themselves and analyse the question of what it means to explain, of how explanations work. That, you may think, is of no concern to you. After all finding explanations is my job. But, we are in the same boat, as explanations are, obviously, closely linked to how we understand. In this context, we will encounter rules, that will be very simple in their structure, but lead to very complicated consequences. Understanding has more to do with the complicated consequences than with the simple rules. This is what makes explaining and understanding difficult. In fact, we will even see, that those complicated consequences cannot really be understood at all, but that we rather just get used to them. Understanding is therefore an inappropriate vocabulary to describe what we are about to do in this book, and so is explaining. This are good news, as now, there cannot be anything in the book that cannot be understood. You just have to get used to it. That, I think, should be doable.

Nonetheless, we will then embark on a search for explanatory models through the history of physics. This search will be successful because we will find the only true, the ultimate language for an objective description of nature. What language might this be?

With this language we will explore how classical physics uses the quantities space and time. We will wonder why it takes time to move through space. What does time have to do with it? Waves will teach us that space and time have to be treated on an equal footing. Shouldn’t it then take space to move through time? Shouldn’t time depend on how something is moving through space? Shouldn’t time be individual, relative and not absolute?

Time is not what we think it is. We will discover, by looking at a water bottle and by throwing dice, that the flow of time is an illusion. The way physics describes time is fundamentally different from the way we experience it, from what we think time is.

In a slightly more technical chapter, we will learn how different observers can compare their locations and clocks, that is, space and time, with each other and, based on that, how they can converse about their respective views on nature. It is a curious thing that this type of conversations, that such a theoretical argument, will directly lead to the most famous equation of all, E = mc², with all of its dramatic consequences for the real world.

Finally, we will learn how waves force us to treat space and time on an equal footing and how this merges space and time into a union, into spacetime. Waves are, furthermore, responsible for the constant speed of light. Just think of your last visit to the beach. Have you ever wondered why waves seem to always go at the same speed? Have you ever asked yourself,

Frage nie, wozu braucht man das, es ist ein Zeichen niederer Gesinnung, August Schmid (1931-2010), aus Die goldenen Worte von Talamone.

Chapter 2

Explanation and Comprehension

In this book, physics and in particular the quantities space and time shall be explained. The nature of explanations is therefore the very first question we have to wonder about. What does it mean to explain something? What makes an explanation an explanation? When is an explanation accepted as an explanation and does this acceptance depend on the person that wants to understand? It may come as a surprise that explanations require explanations. However, it is important to think about this carefully before diving into the world of science itself. In general, this chapter will serve as a reality check for statements like: ’I want to know what is really going on’, where the emphasis is on the word ’really’. This statement expresses the desire for a good and simple explanation, an explanation that is easy to understand.

This chapter is inspired by a video, where Nobel Price winning physicist Richard P. Feynman (1918-1988) is asked to explain magnets and how they repel each other. The question is formulated as follows: I would like to know what’s going on between the two magnets. Search for Feynman and magnets on the web and watch the 7 minutes clip, in which Feynman responds with an endless (well, 7 minutes) cascade of why questions, starting with aunt Minnie and ending with electromagnetism. The video contains much of what I would like to talk about here.

2.1 What is an explanation?

First of all, this chapter will not be a scientific treatise of the terms explanation and comprehension. Instead, we will have a rather loose discussion in which neither the arguments nor the conclusions will be very precise. It is simply a matter of getting a rough idea of what we can expect from an explanation.

We will try to formalize this chapter’s ideas by organizing explanations according to their level of abstraction. This will be particularly interesting as we get to their lowest, most abstract, levels. These form the basis for scientific theories. They are their starting points, their fundamental components. But, if scientific theories are our tool to explain the world, how do we explain their basic components then? If a scientific theory were able to do that, it would basically explain the reason for its own existence. It would be a self-contained theory.

This kind of self-reference is tricky and will almost always get you into trouble. A simple example of a self referential statement is I am lying. The problem with this statement is that it is neither true nor false. Because when I lie, I am telling the truth, and when I tell the truth, I am lying.

A theory about nature is therefore not able to explain everything it contains, for it can’t explain it’s own starting point. Now, only with this simple insight should it dawn on you that explanations are not quite as straight forward as you might have thought.

Let’s take a look at an example to see why a chapter on explanations is important. The point of this book is to learn, why time slows down for moving objects. This phenomenon is part of the theory of special relativity and you will have heard of it. I know from my own experience that it is very difficult to explain this behaviour of time to a layman. As you start explaining, people will be able to follow your line of reasoning at first, whereas in the end, I am certain, they cannot help the feeling that nothing has really been explained. The mathematical explanations are not overly complicated though as they come from linear algebra, which you may even have studied in school, a subject not exactly notorious for its complexity. Why is it so difficult then to explain this behavior of time? The problem, as we will see, is not so much the explanations themselves, but rather your unrealistic expectation, of what they are supposed to provide.

Explanations about the behavior of time are especially tricky. There are two reasons for it:

Firstly, time is one of the basic components of scientific theories. This theories therefore do not contain any explanation of what time actually is. Really? Is physics based on undefined quantities? Don’t worry, this is not really the case and we shall see later, how physics copes with this issue.

Secondly, people have very precise ideas of what they think time is, even if they are not able to give a proper definition. The philosopher Augustine of Hippo (354-430) put it this way: What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.

We are exposed to time literally every second of the day. Clocks are our servants and our masters. They tell us how to organize our day. The invention of clocks has accelerated the pace of our lives. Die Uhr hat uns die Zeit gestohlen, (The clock has stolen our time), August Schmid (1931-2010), mathematician. We perceive time as flowing, that there is a past, a present and a future, and that the flow of time is directed towards the future.

For us, time doesn’t feel linear. We have a personal interpretation of the speed of time. When enjoying ourselves, time seems to fly by, while on other occasions it feels as if time is dragging on forever. I would like to quote my children here: ’Going to bed on time is way too early’.

However, there is a problem with the notion of a flowing time. According to physics, it is wrong. The experience of the flow of time is not real, but an illusion generated by our brain. We shall see later that the reason for this illusion has to do with the fact that our brain is big, that it is a macroscopic object. This is a mind blowing statement. It was presented in a somewhat nonchalant way. So I would like to repeat it again, in case you are confused, in case you are wondering if you have misunderstood something, in case you are wondering if you have missed something:

Augustine of Hippo would have done better to say: Don’t even bother not to ask me, I do not know what time is.

This prejudice of a time that is perceived as flowing, stands in the way of understanding the way physics describes it. One might think that the understanding of time would be easier for a physicist. All a physicist has to do is to look at the formulas that describe the behavior of time. That’s it, done. Unfortunately, it doesn’t work that way. I can still remember the first time I was taught about the slowing down of time in school. I could have given a thousand reasons why all this could not be true. For one, I thought, if the teacher, Herr Ulmer, can demonstrate how clocks slow down, then why doesn’t he show me how a human body slows down the aging process as well. Today I know, that I don’t have to worry about individual objects and their relationship to time. It is the geometry of spacetime itself that is responsible for the slowing down of time. Since all objects we know obviously live in spacetime, all objects have to follow the rules of spacetime. And the rule is: for moving objects time slows down.

To this day, however, I find it difficult to get used to the idea of the slowing down of time, since it is tricky not to get things confused with our everyday prejudices of it. In this sense, the slowing down of time is not something that can be immediately understood. On the contrary, it is a slow process of becoming accustomed to the idea, to sort of turn it into an everyday experience, so to speak, by reading and thinking about it often enough.

A short side note. It might seem strange that we measure time in units of 60 and not 10. One hour corresponds to 60 minutes and not 10 or 100. There is no kilominute or centihour. Why? Because 60 is a fantastic number. It can be divided by 2, 3, 4, 5 and 6. Therefore, 60 can easily be divided into many different time intervals of equal length.

In the next section, now that we have thought about explanations, we will look at how the process of understanding works.

2.2 To understand, as I understand it

The counter part of explaining, on your side, is understanding. Let us examine what understanding means. To do so, we want to divide the meaning of the word ’to understand’ into two subcategories. This two subcategories are not clearly separate from one another, but rather represent the extreme endpoints